{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:RHCAOBFYT65YZZTPQVUGQ3MXPG","short_pith_number":"pith:RHCAOBFY","canonical_record":{"source":{"id":"1301.3233","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-01-15T06:24:44Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"5baef9773705ceb7b2e181f2a3f5bf71cb6008ef7b98baa35a372be51d4c5a8a","abstract_canon_sha256":"8cb2beafa64089c8ca81fd29ffcd1f47a8be3fde70711607f2ebcad504c18ccd"},"schema_version":"1.0"},"canonical_sha256":"89c40704b89fbb8ce66f8568686d9779a699cea9e318a918984e03667fca2881","source":{"kind":"arxiv","id":"1301.3233","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.3233","created_at":"2026-05-18T02:29:17Z"},{"alias_kind":"arxiv_version","alias_value":"1301.3233v3","created_at":"2026-05-18T02:29:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.3233","created_at":"2026-05-18T02:29:17Z"},{"alias_kind":"pith_short_12","alias_value":"RHCAOBFYT65Y","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"RHCAOBFYT65YZZTP","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"RHCAOBFY","created_at":"2026-05-18T12:27:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:RHCAOBFYT65YZZTPQVUGQ3MXPG","target":"record","payload":{"canonical_record":{"source":{"id":"1301.3233","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-01-15T06:24:44Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"5baef9773705ceb7b2e181f2a3f5bf71cb6008ef7b98baa35a372be51d4c5a8a","abstract_canon_sha256":"8cb2beafa64089c8ca81fd29ffcd1f47a8be3fde70711607f2ebcad504c18ccd"},"schema_version":"1.0"},"canonical_sha256":"89c40704b89fbb8ce66f8568686d9779a699cea9e318a918984e03667fca2881","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:29:17.683436Z","signature_b64":"MfOHdhpRYapM7ine/oPZx1Kmu21ZBrljS/8iYh2Z5P8YG9/ZwbuXIq/ucDO0rWU9OCxRjN9Wx5AfrPdCybQUBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"89c40704b89fbb8ce66f8568686d9779a699cea9e318a918984e03667fca2881","last_reissued_at":"2026-05-18T02:29:17.682835Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:29:17.682835Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1301.3233","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:29:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SFyxlvz8Psmixg+Lct3A+TWmuc4QLJSzYfo9WgEmmUN8UMox00H0/Aw6HLoqsL/L3Ar/346YoHQ9mI6CnFYlAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T22:59:32.017460Z"},"content_sha256":"b5e572b569e488054b2a236f38e22d5749cd0f554c0d623e648bb054cbdde69d","schema_version":"1.0","event_id":"sha256:b5e572b569e488054b2a236f38e22d5749cd0f554c0d623e648bb054cbdde69d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:RHCAOBFYT65YZZTPQVUGQ3MXPG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Shimura curve of discriminant 15 and topological automorphic forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AT","authors_text":"Tyler Lawson","submitted_at":"2013-01-15T06:24:44Z","abstract_excerpt":"We find defining equations for the Shimura curve of discriminant 15 over Z[1/15]. We then determine the graded ring of automorphic forms over the 2-adic integers, as well as the higher cohomology. We apply this to calculate the homotopy groups of a spectrum of \"topological automorphic forms\" associated to this curve, as well as one associated to a quotient by an Atkin-Lehner involution."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.3233","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:29:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wNNnW/g4soG25aOU46W7DL3fjgmNh4LKUUMZRY5KV6IbNvG6P0imlVMzcmkKY2LnHBu4Xj9By9NiQMNws/srDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T22:59:32.018109Z"},"content_sha256":"60ea101c380b11590419b3215e385bfe0f6a6b22c29263d3986d5790b91805d9","schema_version":"1.0","event_id":"sha256:60ea101c380b11590419b3215e385bfe0f6a6b22c29263d3986d5790b91805d9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RHCAOBFYT65YZZTPQVUGQ3MXPG/bundle.json","state_url":"https://pith.science/pith/RHCAOBFYT65YZZTPQVUGQ3MXPG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RHCAOBFYT65YZZTPQVUGQ3MXPG/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-11T22:59:32Z","links":{"resolver":"https://pith.science/pith/RHCAOBFYT65YZZTPQVUGQ3MXPG","bundle":"https://pith.science/pith/RHCAOBFYT65YZZTPQVUGQ3MXPG/bundle.json","state":"https://pith.science/pith/RHCAOBFYT65YZZTPQVUGQ3MXPG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RHCAOBFYT65YZZTPQVUGQ3MXPG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:RHCAOBFYT65YZZTPQVUGQ3MXPG","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"8cb2beafa64089c8ca81fd29ffcd1f47a8be3fde70711607f2ebcad504c18ccd","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-01-15T06:24:44Z","title_canon_sha256":"5baef9773705ceb7b2e181f2a3f5bf71cb6008ef7b98baa35a372be51d4c5a8a"},"schema_version":"1.0","source":{"id":"1301.3233","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.3233","created_at":"2026-05-18T02:29:17Z"},{"alias_kind":"arxiv_version","alias_value":"1301.3233v3","created_at":"2026-05-18T02:29:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.3233","created_at":"2026-05-18T02:29:17Z"},{"alias_kind":"pith_short_12","alias_value":"RHCAOBFYT65Y","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"RHCAOBFYT65YZZTP","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"RHCAOBFY","created_at":"2026-05-18T12:27:57Z"}],"graph_snapshots":[{"event_id":"sha256:60ea101c380b11590419b3215e385bfe0f6a6b22c29263d3986d5790b91805d9","target":"graph","created_at":"2026-05-18T02:29:17Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We find defining equations for the Shimura curve of discriminant 15 over Z[1/15]. We then determine the graded ring of automorphic forms over the 2-adic integers, as well as the higher cohomology. We apply this to calculate the homotopy groups of a spectrum of \"topological automorphic forms\" associated to this curve, as well as one associated to a quotient by an Atkin-Lehner involution.","authors_text":"Tyler Lawson","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-01-15T06:24:44Z","title":"The Shimura curve of discriminant 15 and topological automorphic forms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.3233","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:b5e572b569e488054b2a236f38e22d5749cd0f554c0d623e648bb054cbdde69d","target":"record","created_at":"2026-05-18T02:29:17Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"8cb2beafa64089c8ca81fd29ffcd1f47a8be3fde70711607f2ebcad504c18ccd","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-01-15T06:24:44Z","title_canon_sha256":"5baef9773705ceb7b2e181f2a3f5bf71cb6008ef7b98baa35a372be51d4c5a8a"},"schema_version":"1.0","source":{"id":"1301.3233","kind":"arxiv","version":3}},"canonical_sha256":"89c40704b89fbb8ce66f8568686d9779a699cea9e318a918984e03667fca2881","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"89c40704b89fbb8ce66f8568686d9779a699cea9e318a918984e03667fca2881","first_computed_at":"2026-05-18T02:29:17.682835Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:29:17.682835Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MfOHdhpRYapM7ine/oPZx1Kmu21ZBrljS/8iYh2Z5P8YG9/ZwbuXIq/ucDO0rWU9OCxRjN9Wx5AfrPdCybQUBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:29:17.683436Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.3233","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b5e572b569e488054b2a236f38e22d5749cd0f554c0d623e648bb054cbdde69d","sha256:60ea101c380b11590419b3215e385bfe0f6a6b22c29263d3986d5790b91805d9"],"state_sha256":"d5e5bf4d8cea82901d246d67f85c3ad901cbde4add3c753e745bec7ca739c8b3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M4D2Svmh6u+ZhzQQQPt0YHVsvDGAuWRAIa+g/wwgjFjNz24E0LanjtPKX4fLVZ8V/OY2E++aUttTOxLACzALAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T22:59:32.021688Z","bundle_sha256":"ff2e7a4713075f9549cd03daee61d635b10a367c40f6147fdc8ecead68e05cad"}}